The 19-year-old from Leicester burst into tears when host Cat Deeley revealed she had won the most votes from the public on the BBC1 talent contest.
She said she would "never forget" the experience after winning the £100,000 prize and the chance to perform in Hollywood.
An emotional Charlie said she was "absolutely speechless", fighting back the tears to add: "Thank you so much. I did it."
Tommy Franzen came second, while Lizzie Gough came third after an action-packed final which saw the three finalists take to the stage for six routines each.
Pop star Robbie Williams also performed his new single Morning Sun, which is the official Sport Relief single and released next month.
Judge Nigel Lythgoe praised Charlie's "journey" and said she "grew" throughout the series.
"I think Charlie edged it tonight," he said. "I am going to be so delighted to take her to America and show her to everybody."
Asked what she would remember about the competition, Charlie replied: "Absolutely everything. I will never forget this."